$5.$ Problems and Applications Q$5$

Synergy and Dynaco are the only two firms in a specific high$-$tech industry. They face the following payoff matrix as they decide upon the size of their research budget:

Synergy's DecisionLarge BudgetSmall BudgetDynaco's DecisionLarge Budget$$30$ million,$$$$20$ million$$70$ million,$$$$0$Small Budget$$0,$$$30$ million$$50$ million,$$$$40$ million

If Synergy believes Dynaco will go with a large budget, it will choose a$$budget$.$ If Synergy believes Dynaco will go with a small budget, it will choose a$$budget$.$ Therefore, Synergy$$a dominant strategy.

If Dynaco believes Synergy will go with a large budget, it will choose a$$budget$.$ If Dynaco believes Synergy will go with a small budget, it will choose a$$budget$.$ Therefore, Dynaco$$a dominant strategy.

True or False: There is a Nash equilibrium for this scenario. $($Hint: Look closely at the definition of Nash equilibrium.$)$

True

False